L16: Escape Velocity Calculator

Learning objective: Calculate escape speed and connect launch speed to total-energy sign in an ideal isolated two-body model.

Select Planet

Mass M (×10²⁴ kg) 5.97

Radius R (×10⁶ m) 6.371

Launch Altitude h above surface (km) 0 km

Escape Velocity

v_esc = √(2GM/R)

11.19 km/s

Minimum speed to escape from surface

v_esc at altitude h

11.19 km/s

v_esc(h) = √(2GM/(R+h))

Energy condition for escape: Total energy ≥ 0
½mv² - GMm/r ≥ 0 → v ≥ √(2GM/r) = v_esc

Three Energy Regimes

v < v_esc

7.91 km/s

E < 0 / Bound

v = v_esc

11.19 km/s

E = 0 / Threshold

v > v_esc

15.00 km/s

E > 0 / Unbound

Path-shape condition: ellipse, parabola and hyperbola describe ideal non-collision inverse-square two-body paths with suitable angular momentum. A radial path is a degenerate case.

Energy Diagram

Escape Velocity Facts

11.2 km/s

Earth

2.4 km/s

Moon

59.5 km/s

Jupiter